Am I a crank?
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From: Lester Zick on 1 Sep 2006 18:04 On Thu, 31 Aug 2006 17:05:50 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <asfef2dp88qp6khme53ttl5kk6ilieuev8(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > >> On Thu, 31 Aug 2006 13:04:44 -0600, Virgil <virgil(a)comcast.net> wrote: >> >> >In article <fd6ef2lhai4j05a73goceh4tveovu0lcvb(a)4ax.com>, >> > Lester Zick <dontbother(a)nowhere.net> wrote: >> >> So definitions in modern math are not true? >> > >> >Nor false. A definition is merely a request to allow one thing to >> >represent another. >> >Even if that other thing does not exist, one can at worst only decline >> >the request. >> >> So now neomathematics is anthropomorphic too? My what a fantastic >> beastie indeed. > >Beats Zick's neo-anti-mathematics every time. It certainly beats Zick's anti-neomathematkers every time. ~v~~
From: Lester Zick on 1 Sep 2006 18:06 On Fri, 01 Sep 2006 14:50:40 EDT, fernando revilla <frej0002(a)ficus.pntic.mec.es> wrote: >> On Thu, 31 Aug 2006 19:20:15 EDT, fernando revilla >> <frej0002(a)ficus.pntic.mec.es> wrote: >> >> >DontBother(a)nowhere.net wrote: >> > >> >> So how exactly do definitions differ from >> >> propositions? >> > >> >In the posts of Jack Markan >> >> I can't recall posts of Jack Markan on the subject. >> >> > and >> Virgil, you have the >> >answer. >> >> No, what I have from Virgil at least is the bald >> assertion that there >> are certain kinds of statements called definitions >> which are not >> subject to proof and certain kinds of statements >> called theorems which >> are subject to proof but no indications whatsoever of >> the difference >> between the two which renders one demonstrable and >> the other not >> except that neomathematikers are too lazy or stupid >> to be taxed with >> demonstrations of truth in the case of definitions >> but nevertheless >> want to enter them in the record and use them as if >> they were true. >> >> > If you give a name to something with >> sense, >> >you have a definition. >> >> And what if you give a name to something with no >> sense? >> >> > Nobody say " a >> horse carriage or >> >motor carriage that may be hired for short journeys" >> >> >usually we say " cab ", that is a definition, an >> agreement >> >( time is gold ! ). Propositions are not agreements. >> >> Both definitions and propositions are however >> statements. >> >> ~v~~ > >Sorry, surely you are being honest in this discussion >but I can guess that there are a lot of problems of >communication even in a non mathematical language. Don't patronize me, sport. If you can't answer the question I actually asked instead of some question you wish I'd then don't reply. ~v~~
From: Lester Zick on 1 Sep 2006 18:07 On 1 Sep 2006 11:21:13 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >Aatu Koskensilta wrote: >> MoeBlee's answer might be considered somewhat more obfuscated than >> necessary. > >My purpose was not to give just an informal explanation, but also to >explain that, and how, this is formalized. The details I included are >important for that purpose. And it would be even nicer if they addressed the question I actually asked instead of some question you wish I'd asked instead. ~v~~
From: Lester Zick on 1 Sep 2006 18:13 On 1 Sep 2006 12:24:34 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >Lester Zick wrote: > >> It really doesn't matter the form of the statement or >> abstruse reformulations. They all entail predicate combinations and >> predicate interrelations which are either true, false, or ambiguous. > >But that does not entail that there aren't distinctions among such >statements. Of course not. I just asked what the distinctions are that require probitive values in one statement but precludes them in others. And no one seems capable of even addressing that question in direct terms much less answering it. > For example, some are atomic, some are compound, etc. And >one of the distinctions I menioned is that certain statements uphold >the criteria of eliminability and non-creativity Yeah, Moe, look you're just gonna have to get off this particular high horse cause it just ain't gonna fly. I have no idea what you're appealing to with these words and on the face of it they appear ludicrous in the extreme. > and others don't. >Those that uphold those criteria are those that are correctly formed >definitions. Those that do not uphold the criteria are either not >definitions or not correctly formed definitions. And I should care about this because why? ~v~~
From: Lester Zick on 1 Sep 2006 18:16
On 1 Sep 2006 12:21:38 -0700, "Randy Poe" <poespam-trap(a)yahoo.com> wrote: > >Lester Zick wrote: >> On Fri, 01 Sep 2006 09:49:03 +0300, Aatu Koskensilta >> <aatu.koskensilta(a)xortec.fi> wrote: >> >> >Lester Zick wrote: >> >> On 31 Aug 2006 10:54:03 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >> >> >> >>> schoenfeld.one(a)gmail.com wrote: >> >>>> Definitions can be false too (i.e. "Let x be an even odd"). >> >>> That's not a definition. That's just a rendering of an open formula >> >>> whose existential closure is not a member of such theories as PA. >> >> >> >> Which really clears things up for us, Moe. >> > >> >MoeBlee's answer might be considered somewhat more obfuscated than >> >necessary. We can rephrase it without reference to all this formal stuff >> >and simply say that "let x be an even odd" is not a definition, it's >> >just a shorter version "let x be a natural number and further assume >> >that x is both even and odd" which is neither a proposition nor a >> >definition. It's probably the beginning of a - relatively boring! - >> >proof in which it is established that there is no natural that is both >> >even and odd. >> > >> >Definitions in mathematics often appear in the following forms >> > >> > "An X such that P will be called a Q" >> > "By a X we mean a Y" >> > "When P(X,Y) we often say that X glurbles Y" >> > ... >> > >> >One might quibble and say that a definition of that kind might be false >> >if in fact no one will call an X such that P a Q; or if, in fact, the >> >devious author doesn't really mean a Y by X; or if "we" will not, in >> >fact, often say that X glurbles Y when P(X,Y); and so forth. However, >> >such objections ignore the role claims such as above have in >> >mathematical language, acting as they do essentially as stipulations, >> >analogously as one might say "let's call whoever it was who committed >> >this heinous crime 'John Doe'". >> >> Is a stipulation a statement? Is a definition a statement? Is a >> theorem a statement? Then my question remains as to what the >> difference is between or among statements such that one can be true or >> false and others not? Obviously the answer is that there is no such >> difference. > >"Obviously"? Obviously. >Consider the example given above. It constitutes a >definition of the phrase "John Doe" within the context >of some legal process (let's say a trial). Are you prepared >to declare that statement as true or false? I'm not prepared to deal with predicate combinations which are not true, false, or ambiguous. >Compare that to: "The defendant's name is John Doe." >Do you agree that the defendant has a name, and that >there are only two possibilities, that the name is John Doe >or that it is not? This has exactly what bearing on my observation? >Is it really "obvious" to you that "Let's call the defendant >John Doe" must be either true or false? It's really obvious to me that you have no conception what you're trying to reply to. ~v~~ |